Your method may work but it runs the risk of slipping through the servo arm holes and changing the center point.

Those "little metal tubes" are called crimps or ferrules. Basically you put one on your wire, loop the wire through the servo arm or the clevis (more on this later) and then loop it back through the ferrule. Pull it tight and then loop it through the ferrule again.

Using a set of diagonal cutters, crimp the ferrule in about 3 places, not tight enough to cut it, but tight enough to keep the wires in place.

The clevis, you ask? You need some way of adjusting the centering and tightness of the system. Put a clevis and a rigging coupler (that's a piece of threaded rod with a hole in one end) at each rudder horn. Then feed the pull-pull wire through this hole and the threaded part can be used to adjust the tension. Be sure to use a nut on the threaded part to keep it from turning.

And use a keeper on the clevis.

MINNFLYER, please feel free to jump in here with one of your great diagrams.